Adding cloth physics to vertex group
The entire object, was in triangles which also were separated. A cloth simulation with this would never work to start with, neither would a soft-body simulation. Both are based on a interconnected structure/mesh.

Learning something new along the way, this is what i got, i hope it's somewhat close to your goal.


Now regarding what is needed to get there, or at least to a cape that simulates like cloth:



Since the entire object came triangulated and with all faces separate, we need to select the object, go in edit mode with Tab and select all vertices with A first.
Now we can make the object a whole mesh by pressing Alt+N (Merge) -> By Distance

Now the object can be separated into the two main parts, body and cape. For that we hover over a part of the cape and press L which will Select Linked vertices, thus the cape and the shoulder-part of it will be selected.

To really separate the mesh into two objects we need to press P(Separate) and choose Selection. It will create a new object with the selected part.

conveniently renamed the objects "body" and "cape"
The separated objects allow for a much cleaner simulation, as the bigger the mesh simulated, the more calculations needed, but we are not yet done.
The cape can further be split in two parts, namely the shoulder-part and the cape itself. I'd recommend to hide(if not mentioned, hiding per outliner eye symbol) the body first. 
Below a visual demonstration of the steps.

Sideview makes it easier to select only the upper(shoulder) part. Important is to activate "X-Ray" Alt+Z to ensure the entire upper part is selected and not only the us facing part. Pressing P then allows for a separation based on "Selection"
The new object will be the final cape(which we hide for now), the old cape becomes shoulders. And we are left with a hole at the bottom of the shoulders backside.

Face Orientation overlay active here to make the hole easier to see (red is inside)
I would clean up the shoulder parts geometry for a cleaner look, quads and such, but it's not needed for the simulation asked. Closing the hole we end up with this.

The quads along the previous hole, will be used later as location for the pin-group of the cape.
Since the shoulder part is done, we can switch to the cape geometry, as it needs some work before we can work with it. It's gonna be a bit more complicated, so i try to make small steps.
First hide the shoulder part, then make the cape visible, select it and go in the vertex edit mode.
We get rid of one side to reduce a lot of work. For that we go in the top view with Numpad 7 and activate x-ray with Alt+Z.

Then select all vertices on one side of the y-axis and press X Vertices.

Add a mirror modifier and select the Z-axis (situational, here it's Z).

At this point the cape is not usable for simulation, as it has very odd density. So we need to clean this up. Starting with making the cape single-layered. Going along the outer border of the cape, this edge selection needs to be made.


We can see the cape as a 2 layered blanket, the outer is connected to the inner by a border, if we cut away at the border, the layers get structurally separated.
With the border-loop selected we press X Vertices, to delete and at the same time separate the layers. With L (Select Linked) while hovering over a vertex of the left-over faces of the outer layer we select the now separate part(rest of the outer layer), which we then remove with X Vertices. A visual step by step demonstration below.

We are now left with only one layer of faces for the cape, which needs some cleanup, manually with more control, but more time spend here a visual demonstration of some (not all, as repetitive) steps.

The cleaned up and remeshed cape could look something like this.

Again, the settings for the Quad-remesher can be daunting, but results can be great
The mesh having a better topology/density for cloth simulation makes the big difference. We now need to add the pin-group of the cape that will be responsible for fixing the cape to the shoulder-part.

it's possible to add some weight to the sides of the cape going down to stiffen them a bit

visible in weight paint mode, the selected vertices can be assigned a lower value which will be added to the active vertex-group

Back in object mode, we add the cloth simulation to the cape.
Select the preset for silk and add the pin-group to the shape section.

the values are the ones that worked for me.
Finally make the body a collision object. And for later usage it's a good idea to make the body the parent of the shoulders and the shoulders parent of the cape.(Ctrl+P object with the child and parent selected but the parent active)
 
Lastly as already visible in later pictures, add a floor below the princess and make it an collision object as well. Also, wind, nearly forgot .. 
The wind object was already in the scene, BUT it was too weak, and also not interesting enough, just like a hairdryer, on full throttle (still too weak).
So we are setting up the wind like this:

steps should be easy to follow values can vary, but again these worked for me (may be a good starting point)


The final result can be dissected here Princess_with_cape
(I didn't use Blend-exchange as original owner did not use it either, should i get the ok, i'll change to Blend-Exchange)

The cleanup steps i'm gonna add some more info later, hope in the meantime you can work with this.

Happy Blending